On the polynomial equation $P(Q(x_1,\dots ,x_m))=Q(P(x_1),\dots ,P(x_m))$

Arseny Mingajev

We consider the equation $P(Q(x_1,\dots ,x_{\hat{I}}½))=Q(P(x_1),\dots ,P(x_{\hat{I}}½))$ in polynomials over the field of complex numbers and prove that if $\mathrm{deg}(P)>1$, then it is only solva…